The Iraqi administration and its supporters "weren't ready to make sacrifices for the common cause," said Jeffrey, who served as ambassador from 2010-2012.

In addition, Prime Minister Nouri al-Maliki and his government "almost went out of their way to alienate the Sunni Arabs," which is where the militant group is now finding support to some degree and a lack of resistance, he said.

Iraq 'full blown' foreign policy crisis: Expert

Ayham Kamel, Eurasia Group, and Ilan Berman, American Foreign Policy Council, discuss how the U.S will respond to the tensions in Iraq and if the crisis could lead to a state collapse.

Ilan Berman of the American Foreign Policy Council thinks the U.S. doesn't have many good options, particularly since the American electorate doesn't have the appetite for another Gulf War.

"The administration has a full-blown foreign policy crisis on its hands," Berman told "Closing Bell."